[topicmapmail] Re: (COMPOSER v. composer example)

[MARK DRAGAN]

Robert,

Thank you for your question.

>On Fri, Jan 03, 2003 at 07:27:35PM +0000, MARK DRAGAN wrote:
> > A major mathematical tool/approach that TM can heavily leverage is Set
> > Theory, as you know (just getting us on the same page). Topic Map 
>solutions
> > must deal with set theory because, in my opinion TMs ARE sets.
>
>Why? Plz elaborate.
>
>\rho

In response:
First, let me say that I'm not a set theory expert. I'm more of a visionary 
than a nuts and bolts person, but what I have seen of set theory and its 
internal rigor for measuring, comparing, and performing logical operations 
seems very much like what Topic Maps make possible in the organization of 
information and knowledge. It seems that set theory could be leveraged to 
serve TM goals. I believe this is particularly useful because it would 
likely foster, in those advancing TM theory and application, a continuing 
conscious awareness that everything in the TM world is a set. TMs (including 
the special case where it is composed of zero or ones objects) are Sets in 
that they have prescribed boundaries, contents, associations, and other 
relationships between the objects within its sphere. I call these prescribed 
boundaries their context. Their context serves a frame of reference (as used 
in Relativity Theory) for the elements within them. My point is that 
establishing a "COMPOSER vs. composer" naming convention (as mentioned in 
the thread) is more a function of defining the context/set (read "topic") 
itself than its internal associations. Beethoven is a composer in 
such-and-such context, while I am a composer in another context. In my 
opinion, this is one of the most powerful and far reaching aspects of TMs. I 
believe that TMs provide and/or are moving toward providing the tools that 
will enable the defining and leveraging of information and knowledge IN 
CONTEXT (which also means ACROSS CONTEXTS). My main point was to be a 
reminder that, in the new thinking/paradigm that TM enables, every 
discussion about relationships among topic elements should, at least, imply 
"context", just as everything in Physics now requires the acknowledgement of 
any measurement's frame of reference. Using the composer example, the TM 
within which Beethoven is found might have a subtopic/class/etc called 
composer, and also have a context qualification called Major Composer. This 
TM could be compared, using set theory operations that are already a part of 
TM, (no?), with my context with the word composer in it that has no thought 
of, and hence no qualification: Major Composer. The difference will turn up 
that Beethoven is a Major Composer and I am not. I realize that including 
"context-level" definitions for TMs doesn't necessarily make our jobs 
easier, but I do believe it is a model for thinking about the problem domain 
that helps us generate truer-to-life solutions. Notice  that, in this 
construction, "semantics" naturally become usages-in-context, that is the 
use of "composer" in a context becomes its semantics, and that the semantic 
differences can be measured by such factors as additional qualifiers or 
weighting factors. For example, in a TM whose context was a specific book 
about major composers the number of times the word Major and Composer would 
be included might be significantly higher than in a TM about me. A 
comparison of the two weighting factors related to the word composer might 
be enough to indicate (either to me or a search engine), that if one were 
looking for major composers, that the book on major composers would be a 
better source of that information. Context definitions (sets) could be used 
as the formulae for web searches and finding the degree of semantic 
similarities of information, etc. etc.

I hope that this helps. I'm sorry that I'm not able to provide an extensive 
application of set theory, if that is really what you were after, though I'd 
be happy to contribute more at this level.

Regards,

Mark


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